Phase Diagram ofS=1/2 Antiferromagnetic Heisenberg Model on a Dimerized Square Lattice

The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S ( Q ) at zero temperature are investigated for the S =1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. δ c ≃0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below δ c . The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be ≃(δ c -δ ) β with β=0.27±0.04, while the correlation length in the spin gap region is scaled as ≃(δ-δ c ) -ν with ν=1.36±0.05. All of them are different from the estimates in one-dimension, ν=1 and the spin-wave approximation, β=ν =1. Possible relevance of our result for the spin gap behavior in high- T c superconductors is also discussed.